Finite Group Databasebeta

← #34077182

Subgroups — #34077182

Order 19328.

456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012733C211yesmaximal, characteristic, complemented
2#23752145C213yesmaximal, complemented
3#23752135C213yesmaximal, complemented
4#23752134C213yesmaximal, complemented
5#23752128C213yesmaximal
6#23752082C211yesmaximal, characteristic, complemented
7C2×#126×C151C211yesmaximal, characteristic, complemented
8C22×C22⋊D151C2211yescharacteristic
9#18012733—24no—
10C2×C4⋊Dic151C2213yes—
11C2×C4⋊Dic151C2213yes—
12C2×Dic151⋊C4C2213yes—
13C2×Dic151⋊C4C2213yes—
14C2×C22⋊Dic151C2213yes—
15C2×(C2×D151)⋊C4C2213yes—
16C2×(C2×D151)⋊C4C2213yes—
17C151⋊#95C2213yes—
18C151⋊#95C2213yes—
19#126×C151—24no—
20C2×C4⋊C4×C151C2213yes—
21C2×C22⋊C4×C151C2213yes—
22C2×C42×C151C2211yescharacteristic
23C23×D151C2311yescharacteristic
24C2×C22⋊D151—43no—
25C22×Dic151C2313yes—
26C22×Dic151C2313yes—
27C22×Dic151C2311yescharacteristic
28C4⋊Dic151—43no—
29C4⋊Dic151—43no—
30Dic151⋊C4—26no—
31Dic151⋊C4—43no—
32C22⋊Dic151—43no—
33(C2×D151)⋊C4—26no—
34(C2×D151)⋊C4—43no—
35C24×C151C2311yescharacteristic
36C22×C4×C151C2313yes—
37C22×C4×C151C2313yes—
38C4⋊C4×C151—26no—
39C22⋊C4×C151—26no—
40C42×C151D414yescomplemented
41C22×D151—21no—
42C22×D151—23no—
43C22×D151—23no—
44C22⋊D151—44no—
45C2×Dic151—23no—
46C2×Dic151—23no—
47C2×Dic151—23no—
48C2×Dic151—23no—
49C2×Dic151—23no—
50C2×Dic151—23no—
51C2×Dic151—23no—
52C23×C151—21no—
53C23×C151—23no—
54C23×C151—23no—
55C23×C151C2411yescharacteristic
56C2×C4×C151—23no—
57C2×C4×C151—23no—
58C2×C4×C151—23no—
59C2×C4×C151—23no—
60C2×C4×C151—23no—
61C2×C4×C151C2×D416yes—
62C22×C151—43no—
63C22×C151—41no—
64C22×C151—43no—
65C22×C151C22×D411yescharacteristic
66C22×C151H(5,𝔽2)13yes—
67C22×C1512−1+413yes—
68C2×D151—43no—
69C2×D151—41no—
70C2×D151—43no—
71C4×C151—26no—
72C4×C151—43no—
73Dic151—43no—
74Dic151—43no—
75Dic151—41no—
76C2×C151—81no—
77C2×C151#53713yes—
78C2×C151#56011yescharacteristic
79C2×C151#56313yes—
80D151—81no—
81C151#282311yescharacteristic, complemented, Sylow
82#2823—1511nomaximal, Sylow
83C2×#126—1511no—
84C2×#126D15111yescharacteristic, complemented
85#398—1513no—
86#396—1513no—
87#396—1513no—
88#394—1513no—
89#384—1511no—
90C22×D4—1511no—
91#126—24no—
92#126—3024no—
93C2×C4⋊C4—1513no—
94C2×C4⋊C4—1513no—
95C2×C4⋊C4—1513no—
96C2×C4⋊C4—1513no—
97C2×C4⋊C4C2×D15113yes—
98C2×C22⋊C4—1513no—
99C2×C22⋊C4—1513no—
100C2×C22⋊C4—1513no—
101C2×C22⋊C4C2×D15113yes—
102C2×C42C2×D15111yescharacteristic
103#95—1513no—
104#95—1513no—
105C24—1511no—
106C24C22×D15111yescharacteristic
107C2×D4—6043no—
108C22×C4—1511no—
109C22×C4—1513no—
110C22×C4—1513no—
111C22×C4C22×D15113yes—
112C22×C4C22×D15113yes—
113C4⋊C4—26no—
114C4⋊C4—3026no—
115C4⋊C4—6043no—
116C4⋊C4—6043no—
117C4⋊C4—6043no—
118C22⋊C4—26no—
119C22⋊C4—3026no—
120C22⋊C4—6043no—
121C22⋊C4—6043no—
122C42C22⋊D15114yescomplemented
123C23—21no—
124C23—23no—
125C23—23no—
126C23—3021no—
127C23—3023no—
128C23—3023no—
129C23C23×D15111yescharacteristic
130D4—6044no—
131C2×C4—23no—
132C2×C4—23no—
133C2×C4—23no—
134C2×C4—23no—
135C2×C4—23no—
136C2×C4—3023no—
137C2×C4—3023no—
138C2×C4—3023no—
139C2×C4—3023no—
140C2×C4—3023no—
141C2×C4—3023no—
142C2×C4—3023no—
143C2×C4C2×C22⋊D15116yes—
144C22—43no—
145C22—43no—
146C22—41no—
147C22—6043no—
148C22—6043no—
149C22—6041no—
150C22C22×C22⋊D15111yescharacteristic
151C22#1801278513yes—
152C22#1801278613yes—
153C4—26no—
154C4—43no—
155C4—6043no—
156C4—6041no—
157C4—6043no—
158C2—81no—
159C2—12081no—
160C2#2375279013yes—
161C2#2375295311yescharacteristic
162C2#2375296413yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
FittingC2×#126×C151C2
prime radicalC22×C22⋊D151C22
hypercenterC2×#126D151
hypocenterC151#2823
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#126

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#18012733C2semidirect
2. #23752145C2semidirect
3. #23752135C2semidirect
4. #23752134C2semidirect
6. #23752082C2semidirect
7. C2×#126×C151C2semidirect
40. C42×C151D4semidirect
81. C151#2823semidirect
84. C2×#126D151semidirect
122. C42C22⋊D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#180127332
#237521452
#237521352
#237521342
#237521282
#237520822
C2×#126×C1512
#2823151